Evaluation of the J2000 groundwater component

1 Analysis of J2K output

The model was run from the 01.01.1974 until the 31.12.2022.

Figure 1: Ratio of max(actRG1)/maxRG1 and geological units of HRUs

2 Data availability of reference stations

Figure 2: Data availability of reference stations

3 Visual comparison of J2K, AquiFR and ADES

The data was normalized to a range between 0 and 1:

\[ norm(value)=\frac{value-min(value)}{max(value)-min(value)} \] Since the J2K groundwater component is only conceptual and the interest of the analysis lies more on the dynamics and not on the absolute values, the normalized values (norm(value)) were rescaled around the mean value: \[ resc(value) = \frac{norm(value)}{mean(norm(value))} \] For all stations, the starting time was set to the first hydrological year with more than 90% available data. In general, however, a warm-up period of 10 years was considered.

3.1 Time series

Figure 3: Time series of normalized and rescaled values

3.2 Regime

Figure 4: Regime of hydrological year

3.3 Duration curves

Figure 5: Duration curves

3.3.1 Interquartile range

The interquartile range (IQR) is the range between the 25th and 75th percentile, indicating the slope of the duration curve.

Figure 6: Interquartile range (IQR) of the duration curves

4 Goodness-of-fit tests

Table 1: Goodness of Fit tests | J2K - ADES

Variable	Min	1st Qu.	Median	Mean	3rd Qu.	Max
Corr	0.18	0.46	0.66	0.61	0.78	0.87
KGE	-0.72	0.026	0.26	0.25	0.59	0.85
NSE	-4.5	-0.99	-0.075	-0.61	0.36	0.75
mse	0.068	0.17	0.22	0.28	0.32	0.94
rmse	0.26	0.41	0.47	0.5	0.56	0.97

Table 2: Goodness of Fit tests | J2K - AquiFR

Variable	Min	1st Qu.	Median	Mean	3rd Qu.	Max
Corr	0.034	0.44	0.66	0.59	0.78	0.94
KGE	-6.4	0.0023	0.24	-0.02	0.58	0.93
NSE	-62	-1.1	0.0069	-2.6	0.24	0.87
mse	0.058	0.14	0.24	0.31	0.39	1.1
rmse	0.24	0.37	0.49	0.52	0.62	1

4.1 Maps

Figure 7: Correlation of J2K output to ADES

Figure 8: KGE of J2K output to ADES

Figure 9: NSE of J2K output to ADES

5 Correlation of the different plots

Figure 10: Correlation of J2K to ADES

6 Comparison of different normalization approaches

6.1 Normalization with percentiles and median

Another approach to normalize the data is to use the 25th and 75th percentile instead of the minimum and maximum. After that the data is rescaled around the median.

\[ norm(value)=\frac{value-25Percentile(value)}{75Percentile(value)-25Percentile(value)} \]

\[ resc(value) = \frac{norm(value)}{median(norm(value))} \]

6.1.1 Time series

Figure 11: Time series of normalized and rescaled values

6.1.2 Regime

Figure 12: Regime of hydrological year

6.2 Normalization with percentiles

Only the normalization with percentiles but no rescaling.

6.2.1 Time series

Figure 13: Time series of normalized values

6.2.2 Regime

Figure 14: Regime of hydrological year

6.3 Normalization with percentiles and mean

Normalization with percentiles but rescaling around the mean.

6.3.1 Time series

Figure 15: Time series of normalized and rescaled values

6.3.2 Regime

Figure 16: Regime of hydrological year

6.4 Z-score normalization

Z-score of a value is calculated with the mean (\(\mu\)) and the standard deviation (\(\sigma\)): \[ norm(value) = \frac{value - \mu}{\sigma} \] This is also the same normalization used for the calculation of the Standardized Precipitation Index (SPI) or the Standardized Piezometric Level Index (SPLI or IPS in french). The SPLI was calculated in the Explore2 project for the output of the model AquiFR and the reference data, and the model was evaluated using the NSE.

6.4.1 Time series

Figure 17: Time series of normalized and rescaled values

6.4.2 Regime

Figure 18: Regime of hydrological year

6.5 Normalization with the minimum and maximum of overlapping period

Same approach as the initial one, but not with the all time minimum and maximum but rather the minimum and maximum of the time period greater then the 50th quantile of the whole time period.

6.5.1 Time series

Figure 19: Time series of normalized and rescaled values

6.5.2 Regime

Figure 20: Regime of hydrological year

It’s really hard to decide visually for one normalization method.

6.6 Euclidean distance between the different normalization approaches and the ADES reference data

The euclidean distance \(dist=\sqrt{\sum{(x-y)^2}}\) was calculated for each approach (\(x\)) to the ADES reference data (\(y\)) for every plot (time series, regime, duration curve). The mean values of all stations are shown in Figure 21.

Figure 21: Mean euclidean distance between the normalization approaches and the ADES data for the different plots

7 Geological parameters of HRUs

From the previous plots it seems, that it is necessary to improve the groundwater component for HRUs with the geological units “Sedimentary - Impermeable” (hgeoID=6) and “Basement - Impermeable” (hgeoID=9). Table 3 shows the original parameters for the hgeoID. RG1_max is very low for both of them and RG1_k is relatively high. It therefore makes sense to increase RG1_max and reduce RG1_k.

Table 3: Geological units and model parameters

hgeoID	Geological unit	RG1_max	RG1_k
1	Alluvium near large rivers	100.0	25
2	Sedimentary - Aquifer - Karst (indifferent tertiary formations)	1050.0	240
3	Sedimentary - Aquifer - Karst/Fissures (limestone)	350.0	420
4	Sedimentary - Aquifer - Partial karst (chalk)	61.2	62
5	Sedimentary - Semi-permeable	76.5	10
6	Sedimentary - Impermeable (Undifferentiated marls)	20.0	120
7	Basement – Aquifer	112.5	20
8	Basement - Semi-permeable (Massif Central metamorphic bedrock)	40.0	15
9	Basement – Impermeable	20.0	225
10	Mountain – Aquifer1	50.0	33
11	Sand and clay	110.0	200
12	Basement (Armorican Massif)	105.0	420
13	Basement - Semi-permeable (metamorphic bedrock)	5.0	200
14	Basement - Semi-permeable	70.0	160
15	Mountain – Aquifer2	120.0	750

8 Decision for z-score normalization

Since the z-score normalization is used for the evaluation of the Explore2 project, it is close to use it for reasons of comparability to use it here too. To unify it the data was monthly aggregated before the normalization. The normalized value is called Standardized Piezometric Level Index (SPLI) in the Explore2 report, which nomenclature will be used from now on. Also the begin of the comparison was set to the year 2004. So there is the most data for all stations available and

Figure 22: Time series of SPLI

For the aggregation to average monthly values, hydrological years with less than 90% data availability were removed.

Figure 23: Regime of hydrological year

Figure 24: Duration curves

Figure 25: NSE(SPLI) of J2K output to ADES

9 Limitations due to the calibration

If you take a look at the plots, two unwanted patterns are recognizable:

• High frequency in time series, resulting in 95th-Percentile = maximum in duration curves \(\rightarrow\) RG1_max is too small
• No variation in time series and values around zero (the mean), resulting in IQR = 0 \(\rightarrow\) RG1_k is too big

These two criteria give the possibility to evaluate/improve the groundwater component of HRUs with no piezometers in them.

10 Evaluation criteria

For further analysis and the calibration of the model to improve the representation of the groundwater component multiple goodness-of-fit tests will be used. Since the main purpose of the model is to simulate the discharge in the Loire catchment, the Kling-Gupta efficiency (KGE) of the square root of the discharge, will be the criterion (also used in Explore2 for J2K model). For the groundwater component two different types of criteria will be used:

• if there are reference piezometers: the Nash-Sutcliffe efficiency of the SPLI, Correlation, time lag of maximum/minimum of the regime
  
• if there are no reference piezometers: difference of 95th-Percentile to maximum and IQR